求解一道prep数学题

傻傻默默熊 · 发表于 2011-2-13 10:11:59

For every positive even integer n, function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, the p is? 求p的范围。答案是大于40

sdcar2010 · 发表于 2011-2-13 11:13:15

This one has been explained before.

Basically,
1) These consecutive natural numbers h(100) and [h(100) + 1] are co-prime, meaning that they do not share any prime numbers as their cofactors.
2) h(100) contains all the prime numbers between 2 (from 2) and 47 (from 94).
3) Then prime numbers among factors of [h(100) + 1] would not include any prime numbers between 2 and 47.
4) Then the smallest prime facotr of [h(100) + 1] is bigger than 47.

求解一道prep数学题

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